Problem: Simplify the following expression: $x = \dfrac{-40q + 20}{45q - 30}$ You can assume $q \neq 0$.
Solution: Find the greatest common factor of the numerator and denominator. The numerator can be factored: $-40q + 20 = - (2\cdot2\cdot2\cdot5 \cdot q) + (2\cdot2\cdot5)$ The denominator can be factored: $45q - 30 = (3\cdot3\cdot5 \cdot q) - (2\cdot3\cdot5)$ The greatest common factor of all the terms is $5$ Factoring out $5$ gives us: $x = \dfrac{(5)(-8q + 4)}{(5)(9q - 6)}$ Dividing both the numerator and denominator by $5$ gives: $x = \dfrac{-8q + 4}{9q - 6}$